<p>A Leslie–Gower predator–prey model is proposed and analyzed in this paper, in which the prey population is affected by the Allee effect and the harvesting effect while predators hunt cooperatively. We use the blow-up method to prove that the origin is an attractor and provide its basin of attraction. The existence and stability of nonnegative equilibria, including two degenerate equilibria, are discussed. Various kinds of bifurcations, such as saddle-node bifurcation, Hopf bifurcation, and Bogdanov–Takens bifurcation, are presented as parameters vary. Numerical simulations are given to validate the primary theoretical findings. The research findings presented in this paper demonstrate that the Allee effect, cooperative hunting, and the harvesting effect significantly influence the dynamic behavior of populations.</p>